The present invention generally relates to a free-form surface generating method, and more particularly to a free-form surface generating method which interpolates an irregular curve mesh including non-uniform rational B-spline (NURBS) curves, with a NURBS boundary Gregory patch with a continuity on a common boundary, and to a shape control method of controlling a shape of a generated surface. This invention can be applied to free-form surface generating processes and to surface shape modification processes performed on a 3-dimensional solid modeler.
Conventional free-form surface generating methods are disclosed in the following publications.
(1) "From Conics To NURBS: A Tutorial and Survey" G. Farin, IEEE Computer Graphics and Applications, Vol.12, No.5, pp.78-86, 1992. PA1 (3) "G.sup.1 Surface Interpolation over Irregular Meshes with Rational Curves" H. Chiyokura, T. Takamura, K. Konno, and T. Harada, NURBS for Curve and Surface Design, G. Farin (Ed.), SIAM, Philadelphia, pp.15-34, 1991. PA1 (4) "Expressing Coons-Gordon Surfaces as NURBS" F. Lin and W. T. Hewitt, IEEE Computer-Aided Design, Vol.26, No.2, pp.145-155, February 1994. PA1 (1) Two surfaces which smoothly join on a common boundary defined by a NURBS curve can be generated. PA1 (2) A complex shape of a surface can be suitably modified by using a simple curve mesh since the common boundary of the surfaces is defined by a NURBS curve. PA1 (3) A visual shape modification is realized by using cross boundary derivative functions and internal control points of the surface. PA1 (4) The NBG patch of the present invention makes it possible to prevent the curve mesh used to generate a fillet surface from becoming complex. PA1 (5) The NBG patch of the present invention makes it possible to smoothly join it with any of a Gregory patch, a rational boundary Gregory patch, a general boundary Gregory patch, and a NURBS surface.
(2) "A New Control Method for Free-Form Surfaces with Tangent Continuity and Its Applications" K. Konno, T. Takamura, and H. Chiyokura, Scientific Visualization of Physical Phenomena, reprint from N. M. Patrikalakis (Ed.), Springer-Verlag, Heidelberg, pp.435-456, 1991.
Various methods of representation of free-form surfaces using NURBS curves and surfaces or the like have been proposed in these publications.
The above publication (1) discloses geometric features of NURBS curves and surfaces and a shape modification method. In this publication, the representation of NURBS curves and surfaces, reparameterization, derivatives, and a shape control method by using control points and weights have been proposed. By using the proposed techniques, the free-form surface generation and shape control using NURBS surfaces can be carried out.
The above publication (2) discloses a shape modification method for free-form surfaces in which a Gregory patch or a general boundary Gregory patch is used. This method involves the concepts of surface interpolation and joining in which cross boundary derivative (CBD) functions are defined, and a shape modification method using the CBD functions.
The above publication (3) discloses a method of generating surfaces joined with a continuity by using the rational boundary Gregory patch.
The above publication (4) discloses a method for expressing a free-form surface by joining three NURBS surfaces. This publication teaches that three NURBS surfaces can be defined by a single NURBS representation.
The method of the above publication (3) teaches the surface interpoplation over irregular curve meshes, including no NURBS curves, with tangent continuity. The method of the above publication (2) teaches the surface interpolation over regular curve meshes, including NURBS curves, with tangent continuity. The method of the above publication (1) teaches the basic evaluation method for handling NURBS curves and surfaces.
However, when the above conventional surface interpolation methods are used, it is difficult to interpolate irregular curve meshes including NURBS curves with the NURBS representation so that free-form surfaces which are joined with tangent continuity on the common boundary are generated.